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General Discussion

Re: If a and b are positive integers, which of the following can
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11 Jun 2013, 02:48

2

In my view, Best approach to such type of questions is to prove that the constraint is possible. Let's see how it works- 1 is odd integer & a, b can take any positive integer value. So if we can prove that any fraction can yield 1, we can reject that choice

Re: If a and b are positive integers, which of the following can
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11 Jun 2013, 03:16

fameatop wrote:

In my view, Best approach to such type of questions is to prove that the constraint is possible. Let's see how it works- 1 is odd integer & a, b can take any positive integer value. So if we can prove that any fraction can yield 1, we can reject that choice

Re: If a and b are positive integers, which of the following can
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11 Jun 2013, 03:30

fameatop wrote:

In my view, Best approach to such type of questions is to prove that the constraint is possible. Let's see how it works- 1 is odd integer & a, b can take any positive integer value. So if we can prove that any fraction can yield 1, we can reject that choiceA. (2+4a)/(4+4b) - Under any condition this can't be odd. AnswerB. (4a)/(b) = 4.1/4 = 1 = OddC. a/b = 4/4 = OddD.(4+a)/(2+4b) = (4+2)/(2+4.1) = 1 = OddE.(4+a)/(1+4b) = (4+1)/(1+4.1) = 1 = OddHope this helps.

Like Flametop has mentioned, I'd like to rephrase the question in a form that 'which of the following can yeild integers'. The expressions are such that one of them under no circumstances can yeild an integer. If one of them always stays a fraction, it can neither be considered odd or even.

Choice 1 can be reduced to \((1 + 2a)/2*(1+b).\)Now for all values of a, the nuemerator will be odd, but the denominator is even (product of 2 and (1+b) which can be even or odd). Hence, the nuemerator and the denom are odd and even respectively, and do not depend on the values of a and b. Hence it will always be a fraction. For the rest of the choices, the value of the expression can be reduced to an integer for some values of a and b. Hence, according to me, the trick is to find the expression whose value is independent of the underlying variables and yeilds a constant value for all cases as above, where the value is a fraction no matter what.

Re: If a and b are positive integers, which of the following can
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11 Jun 2013, 06:33

arpanpatnaik wrote:

fameatop wrote:

In my view, Best approach to such type of questions is to prove that the constraint is possible. Let's see how it works- 1 is odd integer & a, b can take any positive integer value. So if we can prove that any fraction can yield 1, we can reject that choiceA. (2+4a)/(4+4b) - Under any condition this can't be odd. AnswerB. (4a)/(b) = 4.1/4 = 1 = OddC. a/b = 4/4 = OddD.(4+a)/(2+4b) = (4+2)/(2+4.1) = 1 = OddE.(4+a)/(1+4b) = (4+1)/(1+4.1) = 1 = OddHope this helps.

Like Flametop has mentioned, I'd like to rephrase the question in a form that 'which of the following can yeild integers'. The expressions are such that one of them under no circumstances can yeild an integer. If one of them always stays a fraction, it can neither be considered odd or even.

Choice 1 can be reduced to \((1 + 2a)/2*(1+b).\)Now for all values of a, the nuemerator will be odd, but the denominator is even (product of 2 and (1+b) which can be even or odd). Hence, the nuemerator and the denom are odd and even respectively, and do not depend on the values of a and b. Hence it will always be a fraction. For the rest of the choices, the value of the expression can be reduced to an integer for some values of a and b. Hence, according to me, the trick is to find the expression whose value is independent of the underlying variables and yeilds a constant value for all cases as above, where the value is a fraction no matter what.

Hope it helps!

Regards,A

Thank you arpanpatnaik- I like this strategy....was looking for something generic like this!
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